Section 2.2
More Graphs and Displays
1
Section 2.2 Objectives
 Graph quantitative data using stem-and-leaf plots and dot
plots
 Graph qualitative data using pie charts and Pareto charts
 Graph paired data sets using scatter plots and time series
charts
2
Graphing Quantitative Data Sets
Stem-and-leaf plot
 Each number is separated into a stem and a leaf.
 Similar to a histogram.
 Still contains original data values.
Data: 21, 25, 25, 26, 27, 28,
30, 36, 36, 45
2 1 5 5 6 7 8
3 0 6 6
4 5
3
26
Example: Constructing a Stem-and-Leaf
Plot
The following are the numbers of text messages sent last month by
the cellular phone users on one floor of a college dormitory.
Display the data in a stem-and-leaf plot.
155
118
139
129
4
159
118
139
112
144
108
122
126
129
122
78
148
105 145 126 116 130 114 122 112 112 142 126
121 109 140 126 119 113 117 118 109 109 119
133 126 123 145 121 134 124 119 132 133 124
147
Solution: Constructing a Stem-and-Leaf
Plot
155
118
139
129
159
118
139
112
144
108
122
126
129
122
78
148
105 145 126 116 130 114 122 112 112 142 126
121 109 140 126 119 113 117 118 109 109 119
133 126 123 145 121 134 124 119 132 133 124
147
• The data entries go from a low of 78 to a high of 159.
• Use the rightmost digit as the leaf.
 For instance,
78 = 7 | 8
and 159 = 15 | 9
• List the stems, 7 to 15, to the left of a vertical line.
• For each data entry, list a leaf to the right of its stem.
5
Solution: Constructing a Stem-and-Leaf
Plot
Include a key to identify the
values of the data.
6
From the display, you can conclude that more than 50% of the cellular
phone users sent between 110 and 130 text messages.
Graphing Quantitative Data Sets
Dot plot
 Each data entry is plotted, using a point, above a horizontal
axis
 Dots represent an actual data value. Dots representing the
same value are stacked.
Data: 21, 25, 25, 26, 27, 28, 30, 36, 36, 45
26
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
7
Example: Constructing a Dot Plot
Use a dot plot organize the text messaging data.
155
118
139
129
159
118
139
112
144
108
122
126
129
122
78
148
105 145 126 116 130 114 122 112 112 142 126
121 109 140 126 119 113 117 118 109 109 119
133 126 123 145 121 134 124 119 132 133 124
147
• So that each data entry is included in the dot plot, the
horizontal axis should include numbers between 70 and 160.
• To represent a data entry, plot a point above the entry's
position on the axis.
• If an entry is repeated, plot another point above the previous
point.
8
Solution: Constructing a Dot Plot
155
118
139
129
159
118
139
112
144
108
122
126
129
122
78
148
105 145 126 116 130 114 122 112 112 142 126
121 109 140 126 119 113 117 118 109 109 119
133 126 123 145 121 134 124 119 132 133 124
147
From the dot plot, you can see that most values cluster
between 105 and 148 and the value that occurs the most is
126.You can also see that 78 is an unusual data value.
9
Graphing Qualitative Data Sets
Pie Chart
 A circle is divided into sectors that represent categories.
 The area of each sector is proportional to the frequency of each
category.
10
Example: Constructing a Pie Chart
The numbers of motor vehicle occupants killed in crashes in 2005
are shown in the table. Use a pie chart to organize the data. (Source:
U.S. Department of Transportation, National Highway Traffic
Safety Administration)
11
Vehicle type
Cars
Killed
18,440
Trucks
Motorcycles
Other
13,778
4,553
823
Solution: Constructing a Pie Chart
 Find the relative frequency (percent) of each category.
Vehicle type
Frequency, f
Cars
18,440
Trucks
13,778
Motorcycles
Other
4,553
823
37,594
12
Relative frequency
18440
37594
13778
37594
4553
37594
823
37594
 0.49
 0.37
 0.12
 0.02
Solution: Constructing a Pie Chart
 Construct the pie chart using the central angle that
corresponds to each category.
 To find the central angle, multiply 360º by the category's
relative frequency.
 For example, the central angle for cars is
360(0.49) ≈ 176º
13
Solution: Constructing a Pie Chart
Vehicle type
Central angle
Cars
18,440
0.49
360º(0.49)≈176º
Trucks
13,778
0.37
360º(0.37)≈133º
4,553
0.12
360º(0.12)≈43º
823
0.02
360º(0.02)≈7º
Motorcycles
Other
14
Frequency, f
Relative
frequency
Solution: Constructing a Pie Chart
Relative
frequency
Central
angle
Cars
0.49
176º
Trucks
0.37
133º
Motorcycles
0.12
43º
Other
0.02
7º
Vehicle type
From the pie chart, you can see that most fatalities in motor vehicle
crashes were those involving the occupants of cars.
15
Graphing Qualitative Data Sets
Frequency
Pareto Chart
 A vertical bar graph in which the height of each bar represents
frequency or relative frequency.
 The bars are positioned in order of decreasing height, with the
tallest bar positioned at the left.
Categories
16
Example: Constructing a Pareto Chart
In a recent year, the retail industry lost $41.0 million in inventory
shrinkage. Inventory shrinkage is the loss of inventory through
breakage, pilferage, shoplifting, and so on. The causes of the
inventory shrinkage are administrative error ($7.8 million),
employee theft ($15.6 million), shoplifting ($14.7 million), and
vendor fraud ($2.9 million). Use a Pareto chart to organize this
data. (Source: National Retail Federation and Center for Retailing Education,
University of Florida)
17
Solution: Constructing a Pareto Chart
Cause
$ (million)
Admin. error
7.8
Employee theft
15.6
Shoplifting
14.7
Vendor fraud
2.9
From the graph, it is easy to see that the causes of inventory shrinkage
that should be addressed first are employee theft and shoplifting.
18
Graphing Paired Data Sets
Paired Data Sets
 Each entry in one data set corresponds to one entry in a
second data set.
 Graph using a scatter plot.
 The ordered pairs are graphed as
points in a coordinate plane.
 Used to show the relationship
between two quantitative variables.
y
x
19
Example: Interpreting a Scatter Plot
The British statistician Ronald Fisher introduced a famous data set
called Fisher's Iris data set. This data set describes various physical
characteristics, such as petal length and petal width (in
millimeters), for three species of iris. The petal lengths form the
first data set and the petal widths form the second data set. (Source:
Fisher, R. A., 1936)
20
Example: Interpreting a Scatter Plot
As the petal length increases, what tends to happen to the petal
width?
Each point in the
scatter plot
represents the
petal length and
petal width of one
flower.
21
Solution: Interpreting a Scatter Plot
Interpretation
From the scatter plot, you can see that as the petal length
increases, the petal width also tends to increase.
22
Graphing Paired Data Sets
Time Series
 Data set is composed of quantitative entries taken at regular
intervals over a period of time.
 e.g., The amount of precipitation measured each day for one month.
Quantitative data
 Use a time series chart to graph.
time
23
Example: Constructing a Time Series
Chart
The table lists the number of cellular
telephone subscribers (in millions) for the
years 1995 through 2005. Construct a time
series chart for the number of cellular
subscribers. (Source: Cellular Telecommunication &
Internet Association)
24
Solution: Constructing a Time Series
Chart
 Let the horizontal axis represent the
years.
 Let the vertical axis represent the
number of subscribers (in millions).
 Plot the paired data and connect them
with line segments.
25
Solution: Constructing a Time Series
Chart
The graph shows that the number of subscribers has been increasing since
1995, with greater increases recently.
26
Practice Questions
Q(2.5)
The population of federal prisons, according to the most
serious offenses, consists of the following. Make a Pareto chart
of the population.
Violent offenses
Property offenses
Drug offenses
Public order offenses
Weapons
Immigration
Other
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12.6%
8.5%
60.2%
8.2%
4.9%
5.6%
Practice Questions
Q(2.6)
The assets of the richest 1% of Americans are distributed as
follows. Make a pie chart for the percentages.
28
Principal residence
Liquid assets
Pension accounts
Stock, mutual funds, and personal trusts
7.8%
5.0%
6.9%
31.6%
Businesses and other real estate
Miscellaneous
46.9%
1.8%
Practice Questions
Q(2.7)
The age at inauguration for each U.S. President is shown
below. Construct a stem and leaf plot and analyze the data.
57
61
57
57
58
57
61
29
54
68
51
49
64
48
65
52
56
46
54
49
50
47
55
55
54
42
51
56
55
51
54
51
60
62
43
55
56
61
52
69
64
46
54
Practice Questions
Q(2.8)
The data represent the personal consumption (in billions of
dollars) for tobacco in the United States. Draw a time series
graph for the data and explain the trend.
30
Year
1995
1996
1997
1998
1999
2000
2001
2002
Amount
8.5
8.7
9.0
9.3
9.6
9.9
10.2
10.4
Section 2.2 Summary
 Graphed quantitative data using stem-and-leaf plots and dot
plots
 Graphed qualitative data using pie charts and Pareto charts
 Graphed paired data sets using scatter plots and time series
charts
31